刘德志,杨桂元,鲍建海,张伟

• 1:安徽财经大学统计与应用数学学院
• 2:安徽财经大学统计与应用数学学院
• 3:广西工学院信息与计算机科学系
• 4:安徽财经大学统计与应用数学学院 安徽蚌埠233030

摘要(Abstract)：

一般地,对于马尔可夫调制的随机时滞微分系统来说,很难求出其精确解.即使近似解被求出来,因为其复杂的原因也不方便使用.因此,很多数学家引入了很多方法,例如:EM逼近、离散近似逼近、随机泰勒展式等等.由于近似方法不同而有不同的收敛速度.主要研究当漂移系数和扩散系数满足随机泰勒展式时近似解的收敛速度,得出优于EM逼近的方法.

关键词(KeyWords)： 泰勒近似;收敛速度;马尔可夫链;随机

Abstract:

Keywords:

基金项目(Foundation): 安微省教育厅自然科学基金资助项目(KJ2008B011)

作者(Author): 刘德志,杨桂元,鲍建海,张伟

DOI: 10.16393/j.cnki.37-1436/z.2008.02.003

参考文献(References)：

• [1]Jankovic S,Ilic D.An analytic approximation of solutions of stochastic differential equations[J].Computers and Mathematicswith Application,2004,47(6):903-912.
• [2]Basak G K,Bisi A,Ghosh M K.Stability of a random diffusion with linear drift[J].J.Math.Anal.Appl.,1996,202(2):604-622.
• [3]Luo J W.Comparison principle and stability of Ito stochastic differential delay equations with Poisson jump and Markovian switc-hing[J].Nonlinear Analysis,2006,64(3):253-262.
• [4]Luo J W,Zou J Z,Hou Z Z.Comparison principle and stability criteria for stochastic delay differential equations with Mark-ovian switching[J].Sci.China,2003,46(2):129-138.
• [5]Yuan C G,Gloverb W.Approximate solutions of stochastic differential delay equations with Markovian switching[J].Journal ofComputational and Applied Mathematics,2006,194(2):207-226.
• [6]Yuan C G,Mao X R.Robust stability and controllability of stochastic differential delay equations with Markovian switching[J].Automatica,2004,40(2):343-354.
• [7]Yuan C G.Asymtotic Stability in distribution of stochastic differential equations with Markovian switching[J].Stoch.Proc.Ap-pl.,2003,103(4):277-291.
• [8]Yuan C G,Zou J J,Mao X R.Stability in distribution of stochastic differential delay equations with Markovian switching[J].System and Control Letters,2003,50(3):195-207.